Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19127512 | C2 | semidirect |
| 3. #24909173 | C2 | semidirect |
| 4. C2×#19127482 | C2 | semidirect |
| 5. #24907497 | C2 | semidirect |
| 6. #24905568 | C2 | semidirect |
| 7. C83×#2159 | C2 | semidirect |
| 69. M32×C83 | D4 | semidirect |
| 209. #2159 | D83 | semidirect |
| 215. C83 | #13386 | semidirect |
| 269. M32 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917073 | 2 |
| C2×#19127512 | 2 |
| #24909173 | 2 |
| C2×#19127482 | 2 |
| #24907497 | 2 |
| #24905568 | 2 |
| C83×#2159 | 2 |
| #13386 | 83 |